[Paleopsych] Sigma XI: Storied Theory

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Storied Theory
http://www.americanscientist.org/template/AssetDetail/assetid/44518?&print=yes&print=yes

    see full issue: July-August 2005
    Volume: 93 Number: 4 Page: 308
    DOI: 10.1511/2005.4.308

MARGINALIA

Storied Theory

Science and stories are not only compatible, they're inseparable, as shown
by Einstein's classic 1905 paper on the photoelectric effect

    [24]Roald Hoffmann

    Science seems to be afraid of storytelling, perhaps because it
    associates narrative with long, untestable yarns. Stories are
    perceived as "just" literature. Worse, stories are not reducible to
    mathematics, so they are unlikely to impress our peers.

    This fear is misplaced for two reasons. First, in paradigmatic
    science, hypotheses have to be crafted. What are alternative
    hypotheses but competing narratives? Invent them as fancifully as you
    can. Sure, they ought to avoid explicit violations of reality (such as
    light acting like a particle when everyone knows it's a wave?), but
    censor those stories lightly. There is time for experiment--by you or
    others--to discover which story holds up better.

    The second reason not to fear a story is that human beings do science.
    A person must decide what molecule is made, what instrument built to
    measure what property. Yes, there are facts to begin with, facts to
    build on. But facts are mute. They generate neither the desire to
    understand, nor appeals for the patronage that science requires, nor
    the judgment to do A instead of B, nor the will to overcome a
    seemingly insuperable failure. Actions, small or large, are taken at a
    certain time by human beings--who are living out a story.

    Better Theory Through Stories

    One might think that experiments are more sympathetic than theories to
    storytelling, because an experiment has a natural chronology and an
    overcoming of obstacles (see my article, "Narrative," in the
    July-August 2000 American Scientist). However, I think that narrative
    is indivisibly fused with the theoretical enterprise, for several
    reasons.

    One, scientific theories are inherently explanatory. In mathematics
    it's fine to trace the consequences of changing assumptions just for
    the fun of it. In physics or chemistry, by contrast, one often
    constructs a theoretical framework to explain a strange experimental
    finding. In the act of explaining something, we shape a story. So C
    exists because A leads to B leads to C--and not D.

    Two, theory is inventive. This statement is certainly true for
    chemistry, which today is more about synthesis than analysis and more
    about creation than discovery. As Anne Poduska, a graduate student in
    my group, pointed out to me, "theory has a greater opportunity to be
    fanciful, because you can make up molecules that don't (yet) exist."

    Three, theory often provides a single account of how the world
    works--which is what a story is. In general, theoretical papers do not
    lay out several hypotheses. They take one and, using a set of
    mathematical mappings and proof techniques, trace out the
    consequences. Theories are world-making.

    Finally, comparing theory with experiment provides a natural ending.
    There is a beginning to any theory--some facts, some hypotheses. After
    setting the stage, developing the readers' interest, engaging them in
    the fundamental conflict, there is the moment of (often experimental)
    truth: Will it work? And if that test of truth is not at hand, perhaps
    the future holds it.

    The theorist who restates a problem without touching on an
    experimental result of some consequence, or who throws out too many
    unverifiable predictions, will lose credibility and, like a
    long-winded raconteur, the attention of his or her audience. Coming
    back to real ground after soaring on mathematical wings gives theory a
    narrative flow.

    Let me analyze a theoretical paper to show how this storytelling
    imperative works. Not just any paper, but a classic appropriate to the
    centennial of Albert Einstein's great 1905 papers.

    The Puzzle of Dwarvish Work

    Einstein's paper on the photoelectric effect, published that fecund
    year, was singled out by the 1921 Nobel Committee (late as usual, and
    perhaps still afraid of relativity) as the basis for their award. It
    is also the only one of the 1905 papers that Einstein himself deemed
    revolutionary. But when one reads the article, the photoelectric
    effect appears late, as a denouement; the paper begins elsewhere.

    The unwritten prologue is the contemporary interest in black-body
    radiation--the tendency of any object, no matter what its composition,
    to radiate light when it is heated. We see it in iron nestled in the
    forge, glowing red, then yellow, then white.

    The intensity of this emitted light varies with the color
    (wavelength). At low temperatures, bodies radiate in the infrared. As
    the temperature rises, the maximum intensity of the radiated light
    moves into the red, then extends through the spectrum to the
    ultraviolet. At high temperatures, objects radiate intense light
    across the visible spectrum--that's white heat. The intensity of
    radiated light diminishes in the extreme ultraviolet and far infrared
    (see right). Astronomers estimate the temperatures of stars from just
    such curves.

    The standard (and eminently successful) understanding of light in
    Einstein's day came from James Maxwell's electromagnetic theory.
    Coupled with thermodynamics and the kinetic theory of gases--a high
    expression of Newtonian mechanics--electromagnetic theory led to a
    "radiation law" that described how the intensity of light varied with
    wavelength at each temperature. The law fit the data--at long
    wavelengths. At short wavelengths, the equation derived from
    electromagnetic theory failed, in what became known as "the
    ultraviolet catastrophe."

    In 1900, Max Planck found an expression that fit over the entire range
    of observations. Planck further perceived that his accurate radiation
    law could be obtained only if the energies of the little bits of
    oscillating charge that caused the light (he called them "resonators")
    assumed discontinuous values. So the quantum was born.

    Planck had trouble believing that physics was, deep down,
    discontinuous. He spent many years searching for a way around what he
    discovered. But that is another story.

    How Einstein Tells It

    The photoelectric paper is modestly entitled, "On a Heuristic Point of
    View Concerning the Production and Transformation of Light." Einstein
    begins by stating the problem posed by the quantum hypothesis: He
    defines the resonators as bound electrons and takes us, with
    characteristic clarity, made possible by five years of experience with
    quanta, through Planck's derivation. He develops the characters in his
    tale--the radiation, Planck, his resonators, classical electromagnetic
    theory.

    Then Einstein does something new. He sets out to derive Planck's
    radiation law without any assumptions about how light is generated.
    How does he do that? By assigning an entropy (the measure of
    randomness, a concept already in wide use by then) to the light and
    relating that entropy to the density of the radiation. Einstein proves
    that the entropy of the light in the black body varies with volume
    just the way that entropy varies with volume for that standby of
    freshman chemistry, the ideal gas.

    This demonstration is direct. It's not Hemingway, but for scientific
    prose, really exciting. Einstein is taking us somewhere--we don't know
    where yet, but by the way he sets the scene, by his pace and
    conviction, we know something is going to happen.

    Pretty incredible. No resonators, just a functional analogy of atoms
    or molecules to light. Playing out the analogy, light of a given
    wavelength could be described as if its energy came in dollops of
    what Einstein called Rbv/N, and today we would call hv, a constant (h)
    times the light's frequency (v). But that's just a way of looking at
    things--it's not for nothing that Einstein put the word heuristic in
    the title. Or is it? When do stories become real?

    Back to the paper: Einstein has just rederived Planck's radiation law
    without resonators. Yet the discreteness of the light's energy, its
    quantization, is newly manifest in Einstein's work. There is no
    mistaking it. From this climax the paper cruises along another
    plateau, then swoops into a breathtaking shift of scene. Philipp
    Lenard had three years earlier observed "cathode rays," or beams of
    electrons, by shining light onto a metal. The phenomenon happened only
    when the frequency of that light exceeded a certain minimum; below
    that frequency (or above that wavelength)--nothing. After seeing the
    electrons, Lenard observed that their kinetic energy depended on the
    color of the light, their number on the intensity of the light.

    This phenomenon we now call the photoelectric effect. Aside from being
    today a primary source of information on molecules and surfaces, the
    effect is behind photoelectric cells opening elevator doors, and is
    used in solar cells and light-sensitive diodes.

    Back to 1905. Einstein just says: Let's assume light is quantized in
    units of hv, and that a "light quantum" (we would call it a photon
    today) gives up all its energy to a single electron. The electron
    needs a certain energy to leave the surface; if it has some left over,
    the extra contributes to its motion. Einstein calculates, in a couple
    of terse sentences, the energies involved and finds reasonable
    agreement with Lenard's measurements. With this and another
    calculation on the ionization of gases, he brings us down to
    experimental reality.

    Except reality is not down, it is evidence. Evidence that this story
    of light being quantized is not just any story. This one is worth
    telling to our great-grandchildren.

    Einstein's theory leaves us soaring, thinking what else this strange,
    discontinuous view of light might explain. Soon Bohr will use it to
    give us the first theory of an atom. This story is as exciting as
    Thomas Mann's 1902 Buddenbrooks, which Einstein might have been
    reading at the time.

    The photoelectric paper was submitted to Annalen der Physik (Annals of
    Physics) in March 1905. But Planck's quantum theory, and the nature of
    light, had been on Einstein's mind for quite a while. On April 30,
    1901 he wrote to his future wife, Mileva Maric, "I came recently on
    the idea that when light is generated, perhaps there occurs a direct
    conversion of kinetic energy to light. Because of the parallelism:
    motional energy of the molecules--absolute temperature--spectrum
    (energy of radiation in equilibrium). Who knows when a tunnel will be
    dug through these hard mountains!"

    The Story Is in the Theory

    All theories tell a story. They have a beginning, in which people and
    ideas, models, molecules and governing equations take the stage. Their
    roles are defined; there is a puzzle to solve. Einstein sets his
    characters into motion so ingeniously, using entropy to tease out the
    parallels between moving molecules and the energy of light. The story
    develops; there are consequences of Einstein's approach. And at the
    end, his view of light as quantized and particular confronts the
    reality of the heretofore unexplained photoelectric effect. The
    postscripted future, of all else that can be understood and all new
    things that can be made, is implicit.

    Perceptive reader Anne Poduska notes that the photoelectric paper "is
    particularly interesting because of the layering of perspectives
    (similar to legends being passed from one generation to the next, with
    each storyteller adding their own flair/details)." Indeed, Einstein
    uses Planck's development of the radiation law even as the younger
    physicist claims he will do it differently. He parlays belief in the
    discreteness of molecules (some of his contemporaries still doubted
    their existence) into an argument, first cautious, then growing in
    strength, of the discreteness of light.

    A young man of 25, Einstein had mastered the old stories. In this
    paper he combined the ways others looked at the world, and trusting
    analogy as much as mathematics, made something new. Science is an
    inspired account of the struggle by human beings to understand the
    world. Changing it in the process. How could this be anything but a
    story?

    Acknowledgment
    Thanks to Anne Poduska for her careful reading and suggestions.

Bibliography

      * Cassidy, D. 2005. Einstein and the quantum hypothesis. Annalen der
        Physik (series X) 14 (supplement):15-22.
      * Einstein, A. 1905. Über einen die Erzeugung und Verwandlung des
        Lichtes betreffenden heuristischen Gesichtpunkt. Annalen der
        Physik (series IV) 17:132-148. An English translation may be found
        in Ter Haar, D. 1967. The Old Quantum Theory. New York: Pergamon,
        and on the web at
        [30]http://lorentz.phl.jhu.edu/AnnusMirabilis/AeReserveArticles/ei
        ns_lq.pdf
      * Kuhn, T. S. 1978. Black-Body Theory and the Quantum Discontinuity,
        1894-1912. New York: Oxford University Press.

References

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